Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain |
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Authors: | A. F. Hegarty E. O’Riordan |
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Affiliation: | 1.MACSI, Department of Mathematics and Statistics,University of Limerick,Limerick,Ireland;2.School of Mathematical Sciences,Dublin City University,Dublin 9,Ireland |
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Abstract: | A linear singularly perturbed elliptic problem, of convection-diffusion type, posed on a circular domain is examined. Regularity constraints are imposed on the data in the vicinity of the two characteristic points. The solution is decomposed into a regular and a singular component. A priori parameter-explicit pointwise bounds on the partial derivatives of these components are established. By transforming to polar co-ordinates, a monotone finite difference method is constructed on a piecewise-uniform layer-adapted mesh of Shishkin type. Numerical analysis is presented for this monotone numerical method. The numerical method is shown to be parameter-uniform. Numerical results are presented to illustrate the theoretical error bounds established. |
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